Wheel weight vs over all weight.
 

Let say we hove 2 identical cars that weigh 3000 LBS, one has light rims and the other has heavy rims with rear seat delete or any other component to make it stay at 3000 LBS.
Will the fuel economy be affected comparing the 2 cars?

Yes.

Rotational force takes more work to move than static forces. The forty some pounds in the vehicle stands still, while each wheel's weight spins.

I have seen estimates from 4-10 times the weight for rational vs static. I believe there is more detail in other threads, it has been pretty well covered, I just have only picked up so much. The top left corner has a search function, and whatever you want to find can be found that way.

Ok, I've seen this too often. That is just a wishfull belief from people who support lightweight rims. I like lightweight rims, ride on 13lbs, but the reality is that the ratio is about 1.5@rims and maybe 2@tyres.

It entirely depends on driving. At perfect constant speed, fuel economy will be exactly the same (never the case in real life though).
On highway driving, the difference is almost negligible. In city driving, hypermiling techniques are decisive to take advantage of the energy that has been stored in the wheels (even though we never get all the energy back).
I think rotational weight influence is largely overestimated : 4-10 times might only be at full throttle and the overall factor is much lower than that even in city driving.

Where does the energy the shock absorbers absorb come from?

There are 3 weights that you need to contend with and consider in a car design and they are:

#1. Sprung weight
#2. Unsprung weight
#3. Rotational mass

They all have an effect on overall handling and performance. However Unsprung weight will have more of an effect than sprung weight. Rotational mass will have a bigger effect on the acceleration or your car and its overall quickness. Hence is why some cars opt for reduced mass flywheels and lighter drivelines and axles such as the carbon composite or aluminum options.

If you are in a position where you need to make a choice to reduce weight somewhere always first look to reduce unsprung weight then go from there depending on your goals and objectives.

GH :thumbup:

If you have to brake and dissipate the energy, the extra energy stored in heavier rotating parts matters. If you don't, it makes virtually no difference in terms of efficiency; it's still there just stored in a different form.

For a given power input and final stopping point you will accelerate more slowly and decelerate for a longer period of time. You will be slower.

If you want to quantify the rotational energy it depends on the polar moment of inertia of the rotating object. Mass concentrated towards the outside of the rotating object matters more than mass closer to the axis of rotation. Losing a pound of weight off the tire will have more effect than a pound of weight off the wheel.

Are you saying using low profile tire?

Presumably, the tires would be held constant for the purposes of the test. Load rating (# of plys) would vary the weight of identically sized tires.
But rotational energy is a give and take situation, while deviations from a direct path are just take, take, take. Every time you hit a pot-hole, the weight of that corner is lifted by a punch from the sprung mass. Wheel alignment/steering play—same thing.

Where does that energy come from, out of your gas tank?

Here are two interesting links.

1) A rotational mass calculator: Calculate Moment of inertia, Angular Mass Moments - Online Calculation - Physics Calculator

2) A car and driver test of different wheel sizes, showing acceleration, braking, and MPG: Effects of Upsized Wheels and Tires Tested - Tech Dept. - Car and Driver